Period-adding and spiral organization of the periodicity in a Hopfield neural network

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This work reports two-dimensional parameter space plots, concerned with a three-dimensional Hopfield-type neural network with a hyperbolic tangent as the activation function. It shows that typical periodic structures embedded in a chaotic region, called shrimps, organize themselves in two independent ways: (i) as spirals that individually coil up toward a focal point while undergo period-adding bifurcations and, (ii) as a sequence with a well-defined law of formation, constituted by two different period-adding sequences inserted between.

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The author thanks Conselho Nacional de Desenvolvimento Cientí fico e Tecnológico (CNPq), Brazil, for financial support.

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Correspondence to Paulo C. Rech.

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Rech, P.C. Period-adding and spiral organization of the periodicity in a Hopfield neural network. Int. J. Mach. Learn. & Cyber. 6, 1–6 (2015).

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  • Hopfield neural network
  • Hyperbolic tangent activation function
  • Lyapunov exponents
  • Period-adding bifurcation